Given a state $s$, and a value function $v^i$ that determines the expected payoff for the i-th agent in that state, can the two definitions below, one of Nash equilibrium and another of Pareto optimality be compared to one another?
Nash equilibrium: $$v^i(s, \pi^i_*, \pi^{-i}_*) \ge v^i(s, \pi^i, \pi^{-i}_*)\ \ \ \forall\ \ i \in \{1, 2, \cdots,N\}$$
Pareto optimality: $$v^i(s, \Pi_\#) \gt v^i(s, \Pi)$$ for atleast 1 agent $i$, and,
$$v^j(s, \Pi_\#) \ge v^j(s, \Pi)\ \ \ \forall\ \ j \in \{1, 2, \cdots,N\}$$
Notation Used
Nash Equlibrium = $(\pi^i_*, \pi^{-i}_*)$
Pareto Optimal stragey = $\Pi_\#$
It can be seen that both concepts are independent in the sense that
a) A Nash equilibrium can be Pareto optimal
b) A Nash equilibrium is not necessarily Pareto optimal
Clarifying your notations would enable us to give a more precise answer